1. ## linear equations...

OK for these next set of questions I am supposed to say whether or not the following equations are linear. my text gives this formula that I am supposed to match the equation with..I don't know I'm not getting it all the way.

well here are the equations..

1. (y''')^2 - 5y' +2y = x^(19)

2. (tan x)y'' + (sin x)^2*y' + (cos x)y = 0

3. x^2*y'' - xy' + 5y^2 = 18

1. This one is of the 3rd order and not linear, because there is no p(x)y term

2. i said this was linear and its of the second order

3. this is of the second order but not linear because there is no q(x) term.

i think the way i looked at these problems is not quite correct, so any help would be appreciated. thanks in advance

oh and the * means multiplication. thanks

2. Originally Posted by slapmaxwell1
OK for these next set of questions I am supposed to say whether or not the following equations are linear. my text gives this formula that I am supposed to match the equation with..I don't know I'm not getting it all the way.

well here are the equations..

1. (y''')^2 - 5y' +2y = x^(19)

2. (tan x)y'' + (sin x)^2*y' + (cos x)y = 0

3. x^2*y'' - xy' + 5y^2 = 18

1. This one is of the 3rd order and not linear, because there is no p(x)y term

2. i said this was linear and its of the second order

3. this is of the second order but not linear because there is no q(x) term.

i think the way i looked at these problems is not quite correct, so any help would be appreciated. thanks in advance

oh and the * means multiplication. thanks
Brain not working disregard my post.

3. ok so should i disregard what you posted?

4. Originally Posted by slapmaxwell1
OK for these next set of questions I am supposed to say whether or not the following equations are linear. my text gives this formula that I am supposed to match the equation with..I don't know I'm not getting it all the way.

well here are the equations..

1. (y''')^2 - 5y' +2y = x^(19)

2. (tan x)y'' + (sin x)^2*y' + (cos x)y = 0

3. x^2*y'' - xy' + 5y^2 = 18

1. This one is of the 3rd order and not linear, because there is no p(x)y term

2. i said this was linear and its of the second order

3. this is of the second order but not linear because there is no q(x) term.

i think the way i looked at these problems is not quite correct, so any help would be appreciated. thanks in advance

oh and the * means multiplication. thanks
Dear slapmaxwell1,

If the unknown function and its derivatives only appear to the power 1, then the ordinary differential equation is called linear. Otherwise its non linear. Refer: Differential equation - Wikipedia, the free encyclopedia

1) Correct. The third derivative of y is to the power 2. Hence non linear.

2) Correct. y and its derivatives appear to the power 1. Therefore linear.

3) Correct. There is a $y^2$ term. Therefore non linear.

Hope you understood.